Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}-5x+4y &= -4 \\ -8x+8y &= 1\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-2$ and the bottom equation by $1$ $\begin{align*}10x-8y &= 8\\ -8x+8y &= 1\end{align*}$ Add the top and bottom equations. $2x = 9$ Divide both sides by $2$ and reduce as necessary. $x = \dfrac{9}{2}$ Substitute $\dfrac{9}{2}$ for $x$ in the top equation. $-5( \dfrac{9}{2})+4y = -4$ $-\dfrac{45}{2}+4y = -4$ $4y = \dfrac{37}{2}$ $y = \dfrac{37}{8}$ The solution is $\enspace x = \dfrac{9}{2}, \enspace y = \dfrac{37}{8}$.